A connection between viability theory and l1 optimal control

This paper considers l¹ optimal control problems with full state feedback. In contrast to H^∞ optimal control, previous work has shown that linear l¹ optimal controllers can be dynamic and of arbitrarily high order. However, this paper shows that continuous memoryless nonlinear state feedback performs as well as dynamic linear state feedback. The derivation, which is non-constructive, relies on concepts from viability theory